Natural extensions for the Rosen fractions

Authors:
Robert M. Burton, Cornelis Kraaikamp and Thomas A. Schmidt

Journal:
Trans. Amer. Math. Soc. **352** (2000), 1277-1298

MSC (2000):
Primary 11J70, 37A25

DOI:
https://doi.org/10.1090/S0002-9947-99-02442-3

Published electronically:
October 15, 1999

MathSciNet review:
1650073

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Abstract | References | Similar Articles | Additional Information

Abstract: The Rosen fractions form an infinite family which generalizes the nearest-integer continued fractions. We find planar natural extensions for the associated interval maps. This allows us to easily prove that the interval maps are weak Bernoulli, as well as to unify and generalize results of Diophantine approximation from the literature.

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Additional Information

**Robert M. Burton**

Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331

Email:
burton@math.orst.edu

**Cornelis Kraaikamp**

Affiliation:
Technische Universiteit Delft & Thomas Stieltjes Institute of Mathematics, ITS (SSOR), Mekelweg 4, 2628 CD Delft, the Netherlands

Email:
c.kraaikamp@its.tudelft.nl

**Thomas A. Schmidt**

Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331

Email:
toms@math.orst.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02442-3

Received by editor(s):
August 1, 1997

Published electronically:
October 15, 1999

Additional Notes:
The first author was partially supported by AFOSR grant 93-1-0275 and NSF grant DMS 96-26575. The third author was partially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)

Article copyright:
© Copyright 1999
American Mathematical Society